Open AccessStrict Lyapunov functions and feedback controls for SIR models with quarantine and vaccination
Author(s) -
Hiroshi Ito,
Michael Malisoff,
Frédéric Mazenc
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022029
Subject(s) - lyapunov function , quarantine , control theory (sociology) , stability theory , vaccination , function (biology) , lyapunov exponent , stability (learning theory) , dynamics (music) , mathematics , lyapunov redesign , computer science , medicine , control (management) , biology , virology , psychology , physics , ecology , artificial intelligence , nonlinear system , evolutionary biology , pedagogy , quantum mechanics , machine learning , chaotic
We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals.